Core Concepts
The core message of this article is to propose a tractable safety verification scheme for interconnected nonlinear systems, leveraging assume-guarantee contracts and sum-of-squares techniques. The authors develop a contract negotiation approach that exploits the interconnected structure to mitigate the numerical scalability issue in safety verification.
Abstract
The article proposes a safety verification scheme for interconnected nonlinear systems based on assume-guarantee contracts (AGC) and sum-of-squares (SOS) techniques. The key aspects are:
Subsystem Level:
For each subsystem Gi, the authors construct an invariance assume-guarantee contract Ci = (IW_i, IX_i, IY_i) by synthesizing local (control) barrier functions using SOS programming.
They introduce the notions of maximal internal input set W^* and minimal safe region Q^* for each subsystem.
Interconnected System Level:
The authors propose a contract negotiation scheme to find compatible local contracts Ci that satisfy the contract compatibility condition across the interconnected system.
They present three algorithms for different interconnection structures (acyclic, homogeneous, and general) and analyze their properties in terms of termination, soundness, and completeness.
Examples:
The proposed approach is demonstrated on two examples: vehicle platooning and room temperature regulation.
The key contribution is the development of a compositional safety verification framework that can handle large-scale interconnected nonlinear systems by breaking down the problem into smaller, more tractable sub-problems.